How much feedback is required to achieve the degrees of freedom in ergodic X channel?

This paper aims at investigating the required feedback to achieve the Degrees of freedom (DoF) of X channel. Accordingly, a fixed precoding approach is proposed and is argued can achieve the DoF of such channel, assuming the channel state information is partially available at each transmitter through a feedback mechanism. This is achieved through using the notion of ergodic interference alignment technique. Accordingly, in a Rayleigh fading environment, it is shown a feedback rate of 2 log(p) + Θ(log log(p)) can achieve this DoF, where p is the total transmit power.